Related papers: Fractal Dimension in Nonlinear Wave Dynamics Gover…
In this article we obtain exact solutions of (2+1)-dimensional Boiti-Leon-Pempinelli system of nonlinear partial differential equations which describes the evolution of horizontal velocity component of water waves propagating in two…
Fractal structures naturally emerge in quantum systems whose initial states exhibit spatial discontinuities, a phenomenon first identified by Berry in the paradigmatic case of a particle confined in an infinite potential well. While…
Atomization stretches and folds the liquid-gas interface before fragmenting it into ligaments and droplets, making fractal measures a natural descriptor of the breakup state. We examine this idea in two-dimensional volume-of-fluid direct…
Observations of galaxies over large distances reveal the possibility of a fractal distribution of their positions. The source of fractal behavior is the lack of a length scale in the two body gravitational interaction. However, even with…
This study investigates city dynamics employing a nonextensive diffusion equation suited for addressing diffusion within a fractal medium, where the nonadditive parameter, $q$, plays a relevant role. The findings demonstrate the efficacy of…
We investigate the dynamics of multi-lump waves in a new version of a generalized spatial-symmetric higher-dimensional nonlinear dispersive water wave model using an analytical approach. This involves the proposition of a new…
This study investigates the interconnections between the traditional Fokker-Planck Equation (FPE) and its fractal counterpart (FFPE), utilizing fractal derivatives. By examining the continuous approximation of fractal derivatives in the…
The present work shows a novel fractal dimension method for shape analysis. The proposed technique extracts descriptors from the shape by applying a multiscale approach to the calculus of the fractal dimension of that shape. The fractal…
The fractal dimension of a liquid column is a crucial parameter in several models describing the main features of the primary break-up occurring at the interface of a liquid phase surrounded by the gas-flow. In this work, the deformation of…
Shape is one of the most important visual attributes to characterize objects, playing a important role in pattern recognition. There are various approaches to extract relevant information of a shape. An approach widely used in shape…
Fractional models and their parameters are sensitive to changes in the intrinsic micro-structures of anomalous materials. We investigate how such physics-informed models propagate the evolving anomalous rheology to the nonlinear dynamics of…
We carry out extended symmetry analysis of the (1+2)-dimensional Boiti-Leon-Pempinelli system, which corrects, enhances and generalizes many results existing in the literature. The point-symmetry pseudogroup of this system is computed using…
This paper introduces a scale-invariant methodology employing \textit{Fractal Geometry} to analyze and explain the nonlinear dynamics of complex connectionist systems. By leveraging architectural self-similarity in Deep Neural Networks…
In the absence of governing equations, dimensional analysis is a robust technique for extracting insights and finding symmetries in physical systems. Given measurement variables and parameters, the Buckingham Pi theorem provides a procedure…
Under investigation is a new (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation. The main results are listed as follows: (i) lump solutions; (ii) Interaction solutions between lump wave and solitary waves; (iii) Interaction solutions…
This study develops a unified mathematical framework for the analysis of radial differential equations, revealing a fundamental connection between three distinct classes of problems: the nonlinear Riccati equation, the linear Schr\"odinger…
Here we study a class of second-order nonautonomous differential equations, and the corresponding planar and spatial systems, from the point of view of fractal geometry. The fractal oscillatority of solutions at infinity is measured by…
A stochastic differential equation for the plasma density dynamics is derived, consistent with the experimentally measured distribution and the theoretical quadratic nonlinearity. The plasma density is driven by a multiplicative Wiener…
A nonlinear coupled Choi-Camassa model describing one-dimensional incompressible motion of two non-mixing fluid layers in a horizontal channel has been derived in Ref.1. An equivalence transformation is presented, leading to a special…
Fractal dimensions are tools for probing the structure of quantum states and identifying whether they are localized or delocalized in a given basis. These quantities are commonly extracted through finite-size scaling, which limits the…